EP2435985B1 - Method of quantifying the change of pathologies involving changes in the volume of bodies, especially of tumors - Google Patents

Abstract

A method for quantifying the development of pathologies involving changes in volume of a body represented via an imaging technique, including normalizing gray levels by a midway technique for two images I1 and I2 representing the same scene, resulting in two normalized images I′1 and I′2; calculating a map of signed differences between the two normalized images I′1 and I′2; and performing one or more statistical tests based on the assumption of a Gaussian distribution of the gray levels for healthy tissues in the normalized images I′1 and I′2 and/or in the calculated difference map. Advantageously, results of two or more of the tests can be combined for a more specific characterization of the development.

Description

The present invention relates to a method for quantifying the evolution of brain tumors. It applies in particular to the monitoring of the evolution of low-grade gliomas, but more generally to the monitoring of all types of progressive pathologies including imaging methods such as for example magnetic resonance imaging, more commonly referred to as the acronym for MRI, allow monitoring.

It is important, in the context of evolutionary pathologies such as tumors, and especially brain tumors, to be able to appreciate the evolution of these. The determination of the dynamics of evolution of a tumor makes it possible to refine the individual prognosis of a patient, to adjust the means of therapy according to the tumor aggressiveness, or to evaluate the efficacy of the tumor. treatments.

In the particular case of cerebral pathologies, magnetic resonance imaging or MRI is a particularly suitable modality for tumor monitoring; both for the diagnosis of tumors prior to any treatment, as for the assessment of the effectiveness of the treatment. The quantification of the tumor dynamics can therefore be done on the basis of a plurality - at least one pair - of MRI scans. In practice, it is usual to base such an analysis on longitudinal images coming from two MRI modes: the SPGR mode and the FLAIR mode, according to the acronyms for the respective Anglo-Saxon expressions of Spoiled Gradient Recall Echo and Fluid Attenuated Inversion Recovery. It should be noted that other MRI image acquisition protocols exist, and that the following description relates to these particular acquisition protocols only as an example.

It is then possible for a doctor to perform a manual segmentation of the tumor on a selection of different images, in order to assess the spatial extent of the tumor at different cutting levels, at different moments of acquisition of the images, and in at least one of the two aforementioned MRI modes. Such work is relatively tedious, and the appreciation of the tumor dynamics according to this method is relatively dependent on the operator, that is to say that this assessment has a lack of inter-expert reproducibility; even this assessment even shows a lack of intra-expert reproducibility. In other words, the same operator can reach different conclusions based on identical snapshots. This intra-operator variability is estimated at 15%.

It is also possible to proceed to the quantification of the tumor growth according to the technique known in itself of the largest diameters. Nevertheless, this method has certain disadvantages. Some of these drawbacks are related to the orientation of the cutaway shots that may be different from one exam to another. In addition, this method is particularly inadequate following surgery, because of the presence of the operative cavity.

There are methods for automatic determination of tumor dynamics. In particular, there are methods of automatic tumor segmentation, based on relatively complex computational and image processing algorithms, but which are known to provide relatively low reliability and robustness. The variability of the parameters relating to the different MRI examinations that the same patient may undergo, for example the operating parameters of the imaging equipment, the position of the patient's head during the examination, the intrinsic noise phenomena of the imaging apparatus and its environment, lead to contrast differences between the images, making their direct comparison difficult. Thus, nonlinear changes in contrasts between sets of images representing volumes of an area of interest do not make it possible to specifically assess tumor progression, on the basis of simple maps of differences between these images. These differences in contrast make it difficult to automatically compare the images. There are some techniques to standardize gray levels, and to learn longitudinal anatomical variability of noise, so that you can apply corrections to clichés to make them comparable. Nevertheless, these techniques have the disadvantage of imposing repeated MRI scans on the patient, in order to produce accurate noise level maps. Too many MRI exams are of course not desirable, for reasons of high cost and constraints imposed on the patient.

An automatic segmentation is for example described in Vaidyanatham et al .: "Comparison of supervised MRI segmentation methods for tumor volume determination during therapy", Magnetic Resonance Imaging UK, vol. 13, no. 5, 1995, pages 719-728 .

In the example of low grade cerebral gliomas, it is usual to have a first MRI, followed by MRI three months later, where a classification of glioma growth is performed. It is therefore appropriate, for example, to treat a glioma whose growth after three months is typically greater than 2 millimeters, such as a high-grade glioma, and a glioma whose growth after three months is less than 2 millimeters, such as a glioma of low grade. This type of pathology typically exhibits relatively low tumor growth rates, and thus imposes millimetric or even submillimetric quantification techniques. It is also particularly advantageous that these techniques are reproducible, as well as simple and quick to implement.

An object of the present invention is to overcome the aforementioned drawbacks, and to propose a solution to the aforementioned problems.

• une première étape de normalisation de niveaux de gris par une technique mi-chemin de deux images I₁ et I₂ représentant une même scène, c'est-à-dire la même partie anatomique d'un même patient à deux instants successifs, résultant en deux images normalisées I'₁ et I'₂,
• une deuxième étape de calcul d'une carte de différences signées entre les deux images normalisées I'₁ et I'₂,
• une troisième étape comprenant au moins un test statistique se basant sur l'hypothèse d'une distribution gaussienne des niveaux de gris des tissus sains des images normalisées I'₁ et I'₂ et/ou de la carte des différences calculée à la deuxième étape.

To this end, the subject of the invention is a method for quantifying the evolution of pathologies involving changes in body volume represented by an imaging technique, characterized in that it comprises at least:

• a first step of normalizing gray levels by a half-way technique of two images I ₁ and I ₂ representing the same scene, that is to say the same anatomical part of the same patient at two successive instants, resulting in two standardized images I ' ₁ and I' ₂ ,
• a second step of calculating a signed difference map between the two normalized images I ' ₁ and I' ₂ ,
• a third step comprising at least one statistical test based on the assumption of a Gaussian distribution of the gray levels of the healthy tissues of the normalized images I ' ₁ and I' ₂ and / or the difference map computed at the second step .

In one embodiment of the invention, the method of quantifying the evolution of pathologies involving changes in body volume may be characterized in that the first normalization step determines a cumulative histogram of common half-way gray levels. to the two images I ₁ and I ₂ , and equal to the inverse of the arithmetic average of the inverses of the cumulative histograms of gray levels of the two normalized images I ₁ and I ₂ , the two images being normalized by applying the cumulative histogram halfway to the two images I ₁ and I ₂ .

In one embodiment of the invention, the method of quantifying the evolution of pathologies involving changes in body volume may be characterized in that the first normalization step determines a cumulative histogram of common half-way gray levels. to the two images I ₁ and I ₂ , and equal to the inverse of the geometric mean of the inverses of the cumulative histograms of gray levels of the two images I ₁ and I ₂ , the two images being normalized on the cumulated histogram halfway to the two images I ₁ and I ₂ .

et un premier seuil de confiance T₁ de valeur déterminée ;
p(I'_i (x)/µ_i,σ_i) étant la fonction de densité de probabilité pour le niveau de gris I'_i(x) d'un pixel de l'image normalisée I'_i, calculée avec une fonction Gaussienne de moyenne µ_i et d'écart type σ_i de présenter le niveau de gris observé, l'indice 1-2 s'appliquant aux valeurs combinées des images normalisées I'₁ et I'₂, les statistiques pour un pixel donné étant réalisées sur une zone s'étendant autour du pixel sur un nombre déterminé de pixels.In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that a first test compares a generalized likelihood ratio defined by the relation : $$\mathit{GLRT}=\frac{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)},$$

and a first confidence threshold T ₁ of determined value;
p ( I ' _i ( x ) / μ _i , σ _i ) being the probability density function for the gray level I' _i (x) of a pixel of the normalized image I ' _i , calculated with a function Gaussian mean μ _i and standard deviation σ _i to present the observed gray level, the index 1-2 applying to the combined values of normalized images I ' ₁ and I' ₂ , the statistics for a given pixel being performed on an area extending around the pixel over a fixed number of pixels.

et un deuxième seuil de confiance T₂ de valeur déterminée.In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that a second test compares the probability density function. $p\left({\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)/{\mu }_2-{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)$

and a second confidence threshold T ₂ of determined value.

et un troisième seuil de confiance T₃ de valeur déterminée, la fonction F désignant l'intégrale $F\left(t,\mu ,\sigma \right)=1-{\int }_{-t}^t\frac{e^{\frac{-{\left(s-\mu \right)}^2}{2{\sigma }^2}}}{\sqrt{2\pi }\sigma }ds\mathrm{.}$

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that a third test compares the probability value. $F\left(\left|{\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)\right|,0,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)$

and a third confidence threshold T ₃ of determined value, the function F designating the integral $F\left(t,\mu ,\sigma \right)=1-{\int }_{-t}^t\frac{e^{\frac{-{\left(s-\mu \right)}^2}{2{\sigma }^2}}}{\sqrt{2\pi }\sigma }ds\mathrm{.}$

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that the comparison made by the first test carried out in the third step is established by the relation next : $$\ln (\frac{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)}>\mathrm{<figure-callout\; id="1"\; label="ln\; T"\; filenames="imgf0002.png"\; state="\{\{state\}\}">ln\; </figure-callout>}\left(T_{}\right)\left({}_1\right)\mathrm{.}$$

In one embodiment of the invention, the method of quantifying the evolution of pathologies involving changes in body volume can be characterized in that the first confidence threshold T ₁ is equal to 2.

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that the comparison made by the second test performed in the third step is established by the relation next : $$p\left({\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)/{\mu }_2-{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)<{\mathrm{T}}_2,$$

α étant un nombre réel positif non nul paramétrable, et σ _n représentant l'écart type du bruit dans la carte des différences.In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume may be characterized in that the second confidence threshold T ₂ is equal to $\frac{e^{-\alpha }}{\sqrt{2\pi {\sigma }_{\mathrm{not}}^2}},$

α being a positive non-zero realizable number, and σ _n representing the standard deviation of the noise in the difference map.

le troisième seuil de confiance T₃ étant un nombre réel positif non nul très petit devant 1.In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume can be characterized in that the comparison made by the third test carried out in the third step is established by the relation next : $$p\left({\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)/0,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)<{\mathrm{T}}_3,$$

the third confidence threshold T ₃ being a real nonzero positive number very small in front of 1.

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume may be characterized in that the tests carried out in the third step are carried out for all the pixels constituting the normalized images. I ' ₁ and I' ₂ and / or the difference map calculated in the second step.

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume may be characterized in that the tests performed in the third step are performed on the basis of local averages based on pluralities of pixels of the normalized images I ' ₁ and I' ₂ and / or the difference map calculated at the second step forming a plurality of areas covering the normalized images I ' ₁ and I' ₂ and / or the map of the differences.

In one embodiment of the invention, the method of quantifying the evolution of pathologies involving changes in body volume may be characterized in that the first test and / or the second test and / or the third test are performed in the third step, the results of these tests being combined in a fourth step.

In one embodiment of the invention, the method for quantifying the evolution of pathologies involving changes in body volume may be characterized in that said pathology is a brain tumor.

The present invention also relates to a computer program device, characterized in that it implements a method for quantifying the evolution of pathologies involving changes in body volume according to one of the described embodiments. above.

• la figure 1, un ordinogramme illustrant une séquence d'étapes d'un procédé de quantification de l'évolution de tumeurs selon un exemple de mode de réalisation de la présente invention ;
• la figure 2, un ordinogramme illustrant la première étape de normalisation de deux images, selon un exemple de mode de réalisation de la présente invention ;
• la figure 3, des exemples d'images IRM selon deux modes d'imagerie, et de cartes des différences réalisées selon différentes techniques ;
• La figure 4, des exemples d'images IRM représentatives d'une étape de caractérisation de croissance tumorale du procédé selon la présente invention.

Other features and advantages of the invention will appear on reading the description, given by way of example, with reference to the appended drawings which represent:

• the figure 1 a flowchart illustrating a sequence of steps of a method of quantifying the evolution of tumors according to an exemplary embodiment of the present invention;
• the figure 2 a flowchart illustrating the first step of normalizing two images, according to an exemplary embodiment of the present invention;
• the figure 3 , examples of MRI images according to two imaging modes, and maps of the differences made according to different techniques;
• The figure 4 , examples of MRI images representative of a tumor growth characterization step of the method according to the present invention.

The figure 1 presents a flowchart illustrating a sequence of steps of a method of quantifying the evolution of tumors according to an embodiment of the present invention.

For the sake of clarity, we will consider two images of a volume of interest comprising a tumor, taken by MRI in a mode particular operation, at times t ₁ and t ₂ , the instant t ₁ being earlier than the instant t ₂ . It is understood that the method according to the invention can be applied to a plurality of sets of at least two images made according to different modes of MRI operation, taken at least two times. More generally, the method according to the invention can be applied to imaging techniques other than MRI.

It is also understood that a preliminary step, not shown in the figure, and essential for all subsequent processing, is to readjust the two original images taken at times t ₁ and t ₂ , to obtain two images I ₁ and I ₂ , so that pixel-to-pixel common calculations are possible under optimal conditions. Registration techniques are in themselves known from the state of the art, and are therefore not developed in the present description.

With reference to the figure 1 a first step 101 is intended to normalize the images I ₁ and I ₂ . A second step 102 is intended to constitute a map of the differences between the two normalized images in step 101. A third step 103 is intended to perform statistical tests on the basis of the normalized images and / or the difference map. constituted at the step 102. Advantageously a fourth step 104 is intended to exploit the results of the tests performed at the third step 103 to characterize the tumor progression.

The first normalization step 101 makes it possible to overcome the contrast variations between the two images I ₁ and I ₂ .

It is indeed necessary, prior to a comparison between the images I ₁ and I ₂ , to modify these two images in order to bring them to a common radiometry. The radiometry of an image is understood as the dynamics of the gray levels of this image.

A radiometry common to both images makes it possible to focus their comparison on the geometric aspects thereof, representative of the actual state of the area of interest of which these images were made. It is however necessary that such a modification does not modify the geometrical characteristics of the images I ₁ and I ₂ ,.

In order to meet these needs, the present invention proposes to proceed, at the first step 101 of the process of which it is the subject, to a according to the so-called "midway" equalization method, which is still possible to designate by the equivalent Anglo-Saxon term "midway", described in detail hereinafter, with reference to the figure 2 . For an exhaustive description of the half-way equalization method, it is also possible to refer to the article of J. Delon, Midway Image Equalization, Journal of Mathematical Imaging and Vision, 2004. 21 (2): p. 119-134 .

The modifications of the images I ₁ and I ₂ produced during the first step 101 result in two normalized images I ' ₁ and I' ₂ .

The second step 102 makes it possible to establish a map of the differences between the normalized images I ' ₁ and I' ₂ .

A map of the differences between the two normalized images I ' ₁ and I' ₂ is an image whose definition is the same as that of the normalized images I ' ₁ and I' ₂ , but where the gray level of each pixel of this image results from the difference between the corresponding gray levels of the two normalized images I ' ₁ and I' ₂ . It should be noted that it is possible to perform in step 102 a display of the difference map; this imposes a calculation of the absolute value of the differences between the gray levels; on the other hand, for all the calculations explained below, it will be necessary to consider the signed difference between the gray levels of the two normalized images I ' ₁ and I' ₂ .

It is then possible to simply characterize the tumor evolution, for example by counting the pixels of the difference map whose gray level value is greater or less than a predetermined threshold value. Nevertheless, the selectivity of such a simple thresholding method is relatively low. Indeed, even if a map of the differences clearly shows the tumor growth, corresponding to large differences in gray levels between the standardized images I ' ₁ and I' ₂ , the value of these differences is however completely unpredictable. This is because the tumor tissues are relatively heterogeneous in nature, and their nature can vary significantly between two MRI scans. In addition, some brain structures such as ventricles, containing cerebrospinal fluid, and surrounding tissues, such as fats or skull bones, may also exhibit relatively heterogeneous differences in values.

Thus the third step 103 is proposed; this step makes it possible to refine the characterization of the tumoral evolution.

The third step comprises at least one statistical test.

The test carried out at the third step 103 may for example be a first statistical test based on a commonly accepted hypothesis. According to this hypothesis, for so-called normal brain tissues, such as the tissues constituting the white matter, the gray matter and the cerebrospinal fluid, the gray levels of the pixels individually follow Gaussian distributions. Thus, for each pixel of an image - and by extension, for each voxel of the voluminal zone of interest - the gray level values of the pixels of the two normalized images I ' ₁ and I' ₂ can have two configurations.

In a first configuration, these values of gray levels may correspond to the same Gaussian distribution, in which case no change of tissue type has occurred between the instants t ₁ and t ₂ of producing the images of which I ₁ and I ₂ are derived, and thanks to mid-level equalization normalization performed in the first step 101, these gray level values between the two normalized images I ' ₁ and I' ₂ can be directly compared.

In a second configuration, these gray level values may correspond to two different distributions, due to a change in the type of fabric produced between times t ₁ and t ₂ of producing the original photographs.

où I'₁(x) et I'₂(x) sont respectivement les valeurs normalisées de niveaux de gris des pixels correspondants des images normalisées I'₁ et I'₂, (µ_i ,σ _i ) _i=1,2 sont la moyenne et l'écart type de la distribution du pixel correspondant des images normalisées I'_i, et (µ _1-2 ,σ _1-2) sont la moyenne et l'écart type de la distribution des pixels issus des deux images normalisées I'₁ et I'₂, désignés pour la suite pixels combinés des images normalisées I'₁ et I'₂.Thus, the present invention advantageously proposes, in the third step 103, a first statistical test of the Generalized Likelihood Ratio Test (GLRT) test type, in order to characterize the differences in gray levels. according to one or other of the above configurations. The likelihood ratio GLRT for a given pixel can be calculated according to the following relation: $$\mathit{GLRT}=\frac{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)}$$

where I ' ₁ (x) and I' ₂ (x) are respectively the normalized gray level values of the corresponding pixels of the normalized images I ' ₁ and I' ₂ , ( μ _i , σ _i ) _{i = 1,2} are the mean and the standard deviation of the distribution of the corresponding pixel of the normalized images I ' _i , and ( μ _1-2 , σ _1-2 ) are the average and the standard deviation of the distribution of the pixels coming from the two normalized images I ' ₁ and I' ₂ , designated for the following combined pixels of the normalized images I ' ₁ and I' ₂ .

The Probability Density Function, or PDF (Probability Density Function), denoted p ( x / μ _i , σ _i ), is modeled as a Gaussian PDF N ( μ, σ ) entirely characterized by its mean μ and its standard deviation σ. In a general way, and applicable to all the relations in which this term intervenes, this one is given by the following relation: $$p\left(x/\mu ,\sigma \right)=\frac{1}{\sqrt{2\pi }\sigma }{e}^{\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}$$

It should be noted that all the statistics (μ, σ) for the PDFs are estimated locally, in each pixel in zones of nxn pixels. Thus, when reference is made to a test, it should be understood that a plurality of tests, intended to cover the entirety of the pixels constituting the images, are necessary for the implementation of the invention.

This likelihood ratio GLRT is considered to be much greater than 1 in the cases corresponding to the second aforementioned configuration, ie where the assumption of distinct distributions is most likely or in other words, where the levels of Gray pixels of normalized images I ' ₁ and I' ₂ come from different distributions.

It is then possible to appreciate the changes at a pixel by comparing the likelihood ratio with a first confidence threshold T ₁ of determined value.

Advantageously, it can be considered that the change at the level of a pixel is significant if the value of + ln (GLRT) is greater than ln (2), ie: $$\ln (\frac{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{I\text{'}}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{I\text{'}}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)}>\ln \left(2\right)$$

This threshold value takes into account the fact that the PDF product of the numerator of the aforementioned relation (1) implies two standard deviations, whereas only one standard deviation is involved in the denominator of the relation (3).

It is also possible to perform in the third step 103 a second type of statistical test based on the assumption of a Gaussian distribution of the difference map. The principle of this second statistical test is to evaluate the probability that a gray level value of a pixel of the difference map is derived from a Gaussian distribution, on the basis of local individual statistics ( μ _i , σ _i ) _{i = 1.2} specific to the normalized images I ' ₁ and I' ₂ .

Il est alors possible de déduire les statistiques pour un modèle gaussien des différences sur la base des images I'₁ et I'₂, et générer une carte représentative de la probabilité pour que les valeurs actuelles de différences suivent cette distribution. Cette probabilité a donc une valeur d'autant plus élevée que la valeur de différence est bien modélisée par la distribution gaussienne proposée par le modèle, et une valeur d'autant plus faible que la valeur de différence est mal interprétée par le modèle gaussien, ou en d'autres termes, que la modélisation de la différence par une différence de distributions gaussiennes est inappropriée.This second statistical test can be based on the assumption that if pixels representing homogeneous tissues individually have Gaussian distributions, then the corresponding pixels of the map of differences I ' ₂ - I ' ₁ also have Gaussian mean distributions. μ ₂ - μ ₁ and standard deviation $\sqrt{{\sigma }_{}^{}}$$\sqrt{{}_1^2+{\sigma }_2^2}\mathrm{.}$

It is then possible to deduce the statistics for a Gaussian model of the differences on the basis of the images I ' ₁ and I' ₂ , and to generate a map representative of the probability so that the current values of differences follow this distribution. This probability therefore has a value that increases as the difference value is well modeled by the Gaussian distribution proposed by the model, and a value that is smaller as the difference value is misinterpreted by the Gaussian model, or in other words, modeling the difference by a difference in Gaussian distributions is inappropriate.

According to an exemplary embodiment of the invention, it is possible to consider a change at the level of a pixel as significant, if this probability is lower than a second confidence threshold T ₂ .

In order to discriminate between the significant values of the differences, it is necessary to take into account the variability of the grayscale values of the pixels in the homogeneous zones, this variability being due to the noise, and to establish the second confidence threshold T ₂ . It is for example possible to define this second confidence threshold T ₂ definitively, or by proposing to an operator means for adjusting it. This second confidence threshold T ₂ can be used as a control parameter of the type of estimate of tumor growth that is envisaged, for example as a function of the patient's file. Thus, a rather conservative or optimistic estimate of tumor growth can be based on a low value of the second confidence threshold T ₂ , whereas a rather pessimistic estimate can be based on a high value of this threshold.

et ${\sigma }_{n2}^2$

dans les images normalisées I'₁ et I'₂, en estimant la variance dans une zone du fond d'image, c'est-à-dire une zone ne correspondant pas à une structure anatomique mais à de l'air. Il est également possible de considérer une pluralité de zones du fond d'image, et de calculer alors une valeur moyenne de ces variances. Il est ensuite possible de définir la variance ${\sigma }_n^2$

du bruit dans la carte des différences, comme la somme des variances ${\sigma }_{n1}^2$

et ${\sigma }_{n2}^2\mathrm{.}$

In an exemplary embodiment of the invention, it is possible to estimate the noise variance. ${\sigma }_{\mathrm{not}1}^2$

and ${\sigma }_{\mathrm{not}2}^2$

in the normalized images I ' ₁ and I' ₂ , by estimating the variance in an area of the background image, that is to say a zone not corresponding to an anatomical structure but to air. It is also possible to consider a plurality of areas of the background image, and then calculate an average value of these variances. It is then possible to define the variance ${\sigma }_{\mathrm{not}}^2$

noise in the map of differences, as the sum of the variances ${\sigma }_{\mathrm{not}1}^2$

and ${\sigma }_{\mathrm{not}2}^2\mathrm{.}$

où α est un coefficient réel ajustable.It can then be expected to define the second confidence threshold T ₂ by a value determined according to the relation: $$T_2=\frac{e^{-\alpha }}{\sqrt{2\pi {\sigma }_{\mathrm{not}}^2}}$$

where α is an adjustable real coefficient.

Thus, at the end of this statistical test, it can be considered that the changes at a pixel level are significant if the associated PDF function is lower than the second confidence threshold T ₂ , namely: $$p\left({\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)/{\mu }_2-{\mathrm{<figure-callout\; id="1"\; label="\mu "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_1,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)<\frac{e^{-\alpha }}{\sqrt{2\pi {\sigma }_{\mathrm{not}}^2}}$$

The second confidence threshold defined by equation (4) does not reflect a Gaussian white noise model for MRI noise, but rather a model of Gaussian distribution difference values with a mean value of zero and an estimated value of variance of noise.

For example, it is possible to select the appropriate value of the second confidence threshold T ₂ based on the patient's individual data, and restricting tumor growth to a given percentage of the size of the initial tumor. For example, it is possible to start with a zero value of α, then to increase this value in increments of 0.01, until the smallest second confidence threshold T _{2 is} obtained for which the second statistical test carried out at the Third step 103 leads to less than 75% of tumor growth for example, this value being appropriate in the particular case of slow tumor growth linked to a low-grade brain glioma.

qui est comparée à un troisième seuil de confiance de valeur déterminée T₃, avec une sélection des différences significatives quand la probabilité est plus petite qu'un seuil déterminé: Le troisième seuil de confiance T₃ est un réel positif non nul très petit devant 1.In one embodiment of the invention, a third type of statistical test relating to the difference map may be performed in the third step 103, based on the assumption that the average of the differences for a given point, or well for an average value in a given area around this point, is zero. In this third type of test, it is the probability $F\left(\left|{\mathit{I\text{'}}}_2\left(x\right)-{\mathit{I\text{'}}}_1\left(x\right)\right|,0,\sqrt{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="imgf0002.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1^2+{\sigma }_2^2}\right)$

which is compared with a third confidence threshold of determined value T ₃ , with a selection of the significant differences when the probability is smaller than a determined threshold: The third confidence threshold T ₃ is a real positive non-zero very small in front of 1 .

For all the tests described above, the tumor growth can for example be determined on the basis of a tumor initially identified at time t ₁ . The identification of the initial tumor can be performed manually by the practitioner, or according to a known method of automatic segmentation, for example.

It should also be noted that the aforementioned tests can be carried out individually, or combined with each other, so as to offer a better specificity. For example, it is possible to use only the first GLRT-type statistical test, or only the second statistical test based on a Gaussian distribution hypothesis of the difference map, or only the third statistical test based on a hypothesis of equality of difference means, or a combination of the first and second type of test, a combination of the first and third type of test, a combination of the second and third types of test, or a combination of the three types of the above tests.

Other specific statistical tests may be considered: it should be remembered that all the tests are based on a Gaussian distributions assumption at times t ₁ and t ₂ for healthy brain tissues, that is to say other than tissues. constituting the tumor. Some tests also assume that the distributions are the same (either by likelihood as in the first type of test mentioned above, or by equality test averages, as in the third type of test described above).

It should also be noted that the signed differences previously mentioned may also correspond to the difference I ' ₂ - I' ₁ or I ' ₁ and I' ₂ between the normalized images, with the respective means μ ₂ -μ ₁ or μ ₁ -μ ₂ or 0.

In addition, all the tests described above are based on original gray values or differences, or on local average values. In the latter case, it must then be taken into account that the local standard deviation of the values decreases as the inverse of the square root of the number of points taken into consideration.

The fourth step 104 advantageously consists in combining the results of the statistical tests carried out at the third step 103 in order to characterize the tumor growth. This combination makes it possible to confer on the process according to the invention an optimum sensitivity and selectivity. Each of the types of tests described above results for example in an image containing Boolean values. It is thus possible to combine several types of tests by performing the bit by bit, pixel by pixel, of these binary images resulting from the different types of tests.

The figure 2 presents a flowchart illustrating the first step of normalizing two images, according to an exemplary embodiment of the present invention.

It is recalled here that the principle of mid-way equalization, realized in the first step 101 of the method according to the present invention, is to attribute to a pair of images I ₁ and I ₂ a common distribution of levels of Grey. This distribution is defined as a histogram corresponding to a reasonable "half-way", that is to say as the inverse of the average of the cumulative inverse histograms of gray levels of the images I ₁ and I ₂ .

As illustrated on the figure 2 , the image I ₁ is modified by a first contrast change function Φ ₁ , to obtain the normalized image I ' ₁ . In the same way, the image I ₂ is modified by a second contrast-change function Φ ₂ , so as to obtain the normalized image I ' ₂ . The cumulative histogram of gray levels of the image I ₁ is denoted H ₁ , and the cumulative histogram of gray levels of the image I ₂ is denoted H ₂ . The cumulative histograms H ₁ and H ₂ are two increasing functions. According to the mid-level equalization normalization principle, the cumulative histograms of gray levels of the normalized images I ' ₁ and I' ₂ are almost identical. This cumulative histogram is denoted H _midway .

As described in the article by J. Delon supra, contrast change functions Φ ₁ and Φ ₂ such that Φ ₁ (I ₁ ) and Φ ₂ (I ₂ ) have the same cumulative histogram H _midway impose and assume that the following relation is verified: $${\mathrm{\Phi }}_{\mathrm{1}}^{-\mathrm{1}}\circ {\mathrm{\Phi }}_{\mathrm{2}}=H_1^{-1}\circ H_2$$

According to an exemplary embodiment of the present invention, the cumulated mid-way H _midway histogram can then be determined by the following relation: $$H_{\mathit{midway}}={\left(\frac{H_1^{-1}+H_2^{-1}}{2}\right)}^{-1}$$

et $${\mathit{Iʹ}}_2=\frac{I_2+H_1^{-1}\circ H_2\left(I_2\right)}{2}$$

The normalized images I ' ₁ and I' ₂ , which are the images I ₁ and I ₂ that are normalized on the cumulative histogram halfway H _midway , are then given by the following relations: $${\mathit{I\text{'}}}_1=\frac{I_1+H_2^{-1}\circ H_1\left(I_1\right)}{2}$$

and $${\mathit{I\text{'}}}_2=\frac{I_2+H_1^{-1}\circ H_2\left(I_2\right)}{2}$$

Advantageously, it may be envisaged to define the halfway _midway H _midway histogram not by an arithmetic average of the inverses of the cumulated histograms H ₁ and H ₂ , but rather by a geometric mean of these. This embodiment may be appropriate in an application to MRI images, since the non-homogeneities of the field generated by MRI equipment can typically be modeled as multiplicative fields. In other words, the intensity of a pixel of a given image I is in fact formalized by I (x) .g (x), where g is a function of non-homogeneity.

In this way, in this embodiment of the invention, the cumulative histogram halfway H _midway can be determined by the following relation: $$H_{\mathit{midway}}={\left(\sqrt{H_1^{-1}{H}_2^{-1}}\right)}^{-1}$$

et $${\mathit{Iʹ}}_2=\sqrt{I_2\mathrm{.}{H}_1^{-1}\circ H_2\left(I_2\right)}$$

The normalized images I ' ₁ and I' ₂ can then be given by the following relations: $${\mathit{I\text{'}}}_1=\sqrt{{\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="imgf0002.png"\; state="\{\{state\}\}">I</figure-callout>}}_1\mathrm{.}{H}_2^{-1}\circ H_1\left({\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="imgf0002.png"\; state="\{\{state\}\}">I</figure-callout>}}_1\right)}$$

and $${\mathit{I\text{'}}}_2=\sqrt{I_2\mathrm{.}{H}_1^{-1}\circ H_2\left(I_2\right)}$$

It is accepted that the function g (x) is spatially uniform, and that it varies little locally. One can thus make the hypothesis that the function g (x) is comparable to a constant, on restricted spatial zones. It can thus be advantageously envisaged to apply equalization mid-way by small areas of images.

It should be noted that all the calculations presented above apply in the case where two snapshots are available, corresponding to examination instants t ₁ and t ₂ . In the case where the snapshots are available at a plurality N of instants t _N , it is of course possible to transpose the relations (7) to (9), and (10) to (12), using respectively arithmetic means. and geometric, for N inverse cumulative histograms.

The figure 3 presents examples of MRI images of a human brain at a given cutting level, according to two acquisition protocols, and maps of the differences made using different techniques. This figure helps to understand the first step (101) of the method according to the present invention, on the basis of examples from real cases.

A first series of images 300 comprises a first FLAIR image 301 made at time t ₁ according to the IRM FLAIR mode, and a second FLAIR image 302 produced at time t ₂ . Both FLAIR images 301 and 302 are recalibrated.

A first difference map FLAIR 303 is made simply on the basis of a difference between the first two FLAIR images 301 and 302.

A second difference map FLAIR 304 is made on the basis of a difference between the first two FLAIR images 301 and 302, normalized by half-way equalization according to the method of the present invention.

A third difference map FLAIR 305 is made on the basis of a difference between the first two FLAIR images 301 and 302, normalized by a "half-maximum" standardization technique known from the state of the art.

A second series of images 310 comprises a first image SPGR 311 produced at time t ₁ according to the IRM mode SPGR, and a second image SPGR 312 produced at time t ₂ . The two SPGR images 311 and 312 are flunked.

A first difference map SPGR 313 is made simply on the basis of a difference between the first two SPGR images 311 and 312.

A second difference map SPGR 314 is made on the basis of a difference between the first two SPGR images 311 and 312, normalized by half-way equalization according to the method of the present invention.

A third difference map SPGR 315 is made on the basis of a difference between the first two SPGR images 311 and 312, normalized by a "half-maximum" standardization technique known from the state of the art.

The images presented as examples in the figure 3 underline the superiority of the mid-way standardization technique used in the method according to the present invention, compared with techniques known from the state of the art, for the development of difference maps making it possible to highlight tumor growth .

The figure 4 shows examples of MRI images at a tumor zone of a human brain, representative of the third step 103 of the method according to the present invention.

A first series of images 400 is representative of the first type of test as described above, performed in the third step 103. A second series of images 410 is representative of the second type of test as described above, performed in the third step 103.

In the first series of images 400, a first series of images of the first test 401 represents GLRT likelihood ratio maps calculated at the first type of test of the third step 103 of the method of the invention, according to the relation (1 ). A second series of images of the first test after comparison 402 represents the images of Boolean pixels obtained after comparison of the GLRTs with a predetermined value threshold, as formalized by the relation (3). These Boolean pixels represent the significant differences according to the criteria of the first type of test carried out at step 103.

In the second series of images 410, a first series of images 411 of the second type of test represents maps of the probability density functions of the Gaussian differences calculated at the second type of test carried out at the third step 103. A second series of images of the second type of test after comparison 412 represents the images of Boolean pixels obtained after comparison of the aforementioned probability density functions with a predetermined value threshold, as formalized by the relation (5). These Boolean pixels represent the significant differences according to the criteria of the second type of test.

The photographs presented as examples in the figure 4 highlight the characteristic differences of the results obtained via the two types of tests carried out at the third step 103 of the process according to the present invention. In particular, it can be observed in this figure that significant common differences are detected over the whole of the heterogeneous tumor zone, and that the selectivity of the tests is different at the level of the cranial bone zones.

This example further emphasizes the advantage afforded by the fourth step 104 of the method according to the invention, making it possible to combine the two types of tests in order to provide optimum sensitivity and selectivity.

Finally, it should be noted that all the examples presented in the present description apply to brain tumors. However, it is possible to apply the method according to the invention, to the quantification of the evolution of any type of evolutionary pathology whose imaging methods allow monitoring. In particular, the method according to the invention can be applied to the quantifying the evolution of different types of tumors, or bone growth, or even the growth of sclerosis.

The method of the invention can be implemented in any computer program device or device for image analysis and / or diagnostic assistance.

The exploitation of the method according to one of the presented embodiments notably provides the possibility of organizing by imaging a mass screening of any pathology, in particular cerebral, by applying the algorithm to the detection of a difference between an MRI reference and MRI of the patient being tested. In case of anomaly, after rereading by a radiologist, the present invention also allows longitudinal monitoring thereof, in order to adapt the therapeutic strategy in case of scalability.

Claims (16)

1. A method for quantifying the development of pathologies involving changes in volume of a body represented via an imaging technique, characterized in that it comprises at least:

   • a first step (101) for normalization of gray levels by a midway technique for two images I₁ and I₂ representing the same scene, resulting in two normalized images I'₁ and I'₂,

   • a second step (102) for calculation of a map of signed differences between the two normalized images I'₁ and I'₂,

   • a third step (103) comprising at least one statistical test based on the assumption of a Gaussian distribution of the gray levels for the healthy tissues in the normalized images I'₁ and I'₂ and/or in the difference map calculated in the second step (102).
2. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 1, characterized in that the first normalization step (101) determines a midway cumulative histogram of gray levels common to the two images I₁ and I₂, and equal to the inverse of the arithmetic mean of the inverses of the cumulative histograms of gray levels for the two normalized images I₁ and I₂, the two images being normalized by application of the midway cumulative histogram to the two images I₁ and I₂.
3. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 1, characterized in that the first normalization step (101) determines a midway cumulative histogram of gray levels common to the two images I₁ and I₂, and equal to the inverse of the geometric mean of the inverses of the cumulative histograms of gray levels for the two images I₁ and I₂, the two images being normalized on the midway cumulative histogram to the two images I₁ and I₂.
4. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that a first test performs the comparison between a generalized likelihood ratio defined by the equation: $$\mathit{GLRT}=\frac{p\left({\mathit{Iʹ}}_1\left(x\right)/{\mu }_1,{\sigma }_1\right)p\left({\mathit{Iʹ}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{Iʹ}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{Iʹ}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)}$$

   

   
   and a first confidence threshold T₁ of given value;
   p(I'_i (x)/µ_i,σ_i) being the probability density function for the gray level I'_i(x) of a pixel of the normalized image I'_i, calculated with a Gaussian function of mean µ_i and standard deviation σ_i to exhibit the observed gray level, the index 1-2 being applicable to the combined values of the normalized images I'₁ and I'₂,
   the statistics for a given pixel being determined over an area extending around the pixel over a given number of pixels.
5. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that a second test performs the comparison between the probability density function $p\left({\mathit{Iʹ}}_2\left(x\right)-{\mathit{Iʹ}}_1\left(x\right)/{\mu }_2-{\mu }_1,\sqrt{{\sigma }_1^2+{\sigma }_2^2}\right)$

   

   and a second confidence threshold T₂ of given value.
6. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that a third test performs the comparison between the probability value $F\left(\left|{\mathit{Iʹ}}_2\left(x\right)-{\mathit{Iʹ}}_1\left(x\right)\right|,0,\sqrt{{\sigma }_1^2+{\sigma }_2^2}\right)$

   

   and a third confidence threshold T₃ of given value, the function F denoting the integral $$F\left(t,\mu ,\sigma \right)=1-{\int }_{-t}^t\frac{e^{\frac{-{\left(s-\mu \right)}^2}{2{\sigma }^2}}}{\sqrt{2\pi }\sigma }ds\mathrm{.}$$

   
7. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 4, characterized in that the comparison performed by the first test carried out at the third step (103) is established by the following equation: $$\ln (\frac{p\left({\mathit{Iʹ}}_1\left(x\right)/{\mu }_1,{\sigma }_1\right)p\left({\mathit{Iʹ}}_2\left(x\right)/{\mu }_2,{\sigma }_2\right)}{p\left({\mathit{Iʹ}}_1\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)p\left({\mathit{Iʹ}}_2\left(x\right)/{\mu }_{1-2},{\sigma }_{1-2}\right)}>\ln \left(T_1\right)$$

   
8. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 7, characterized in that the first confidence threshold T₁ is equal to 2.
9. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 5, characterized in that the comparison performed by the second test carried out at the third step (103) is established by the following equation: $$p\left({\mathit{Iʹ}}_2\left(x\right)-{\mathit{Iʹ}}_1\left(x\right)/{\mu }_2-{\mu }_1,\sqrt{{\sigma }_1^2+{\sigma }_2^2}\right)<{\mathrm{T}}_2$$

   
10. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 9, characterized in that the second confidence threshold T₂ is equal to $\frac{e^{-\alpha }}{\sqrt{2\pi {\sigma }_n^2}},$

    

    α being a variable non-zero positive real number, and σ_n representing the standard deviation of the noise in the difference map.
11. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in claim 6, characterized in that the comparison performed by the third test carried out at the third step (103) is established by the following equation: $$F\left(\left|{\mathit{Iʹ}}_2\left(x\right)-{\mathit{Iʹ}}_1\left(x\right)\right|,0,\sqrt{{\sigma }_1^2+{\sigma }_2^2}\right)<{\mathrm{T}}_3,$$

    

    
    the third confidence threshold T₃ being a non-zero positive real number much less than 1.
12. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that the tests carried out at the third step (103) are carried out for all the pixels composing the normalized images I'₁ and I'₂ and/or the difference map calculated at the second step (102).
13. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that the tests carried out at the third step (103) are carried out on the basis of local means based on pluralities of pixels from the normalized images I'₁ and I'₂ and/or from the difference map calculated at the second step (102) forming a plurality of areas covering the normalized images I'₁ and I'₂ and/or the difference map.
14. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that the first test and/or the second test and/or the third test are carried out at the third step (103), the results of these tests being combined during a fourth step (104).
15. The method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims, characterized in that said pathology is a brain tumor.
16. A computer program device, characterized in that it implements a method for quantifying the development of pathologies involving changes in volume of a body as claimed in any one of the preceding claims.

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